Silly me, of course they do: http://www.usatoday.com/news/world/story/2012-01-22/mexico-national-voter-ID-cards/52779410/1
Those IDs are a real hoot from what I understand. You can have any name, birthdate, etc put on them that you want on them. All you need is to have two people who already have a card vouch for who you are and when you were born. LOL! Good stuff.
Probably in Mexico, just like in the USA, requiring a photo ID to vote is part of a conspiracy to suppress voting by Hispanics.